import numpy as np
import pandas as pd

# sklearn
from sklearn import metrics
from sklearn.model_selection import train_test_split
from sklearn.datasets import make_moons, make_circles, make_classification
from sklearn.metrics import mean_squared_error, mean_absolute_error

# Pytorch
import torch
from torch.autograd import Variable
import torch.nn as nn 
import torchvision.transforms as transforms

# Visualisation libraries

## Text
from colorama import Fore, Back, Style
from IPython.display import Image, display, Markdown, Latex, clear_output

## progressbar
import progressbar

## plotly
from plotly.offline import init_notebook_mode, iplot 
import plotly.graph_objs as go
import plotly.offline as py
from plotly.subplots import make_subplots
import plotly.express as px

## matplotlib
import matplotlib.pyplot as plt
from matplotlib.font_manager import FontProperties
from matplotlib.patches import Ellipse, Polygon
import matplotlib.gridspec as gridspec
import matplotlib.colors
from pylab import rcParams
%matplotlib inline

## seaborn
import seaborn as sns
sns.set_context('paper', rc={'font.size':12,'axes.titlesize':14,'axes.labelsize':12})
sns.set_style('white')
plt.style.use('seaborn-whitegrid')

import warnings
warnings.filterwarnings("ignore")

PyTorch Artificial Neural Network (ANN)

Dataset

a random n-class classification dataset can be generated using sklearn.datasets.make_classification. Here, we generate a dataset with two features and 6000 instances. Moreover, the dataset is generated for multiclass classification with five classes.

X, y = make_classification(n_samples = int(6e3), n_features=2, n_redundant=0, n_classes = 4,
                           n_informative=2, random_state=1, n_clusters_per_class=1)
Labels = np.unique(y)
Labels = [str(x) for x in Labels]

Modeling

Train and Test sets

One of the efficient methods of splitting a dataset into random train and test subsets is using sklearn.model_selection.train_test_split.

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

pd.DataFrame(data={'Set':['X_train','X_test','y_train','y_test'],
               'Shape':[X_train.shape, X_test.shape, y_train.shape, y_test.shape]}).set_index('Set').T

Set	X_train	X_test	y_train	y_test
Shape	(4200, 2)	(1800, 2)	(4200,)	(1800,)

# Train and Test Tests

if torch.cuda.is_available():
    X_train_tensor = Variable(torch.from_numpy(X_train).cuda())
    y_train_tensor = Variable(torch.from_numpy(y_train).type(torch.LongTensor).cuda())
    X_test_tensor = Variable(torch.from_numpy(X_test).cuda())
    y_test_tensor = Variable(torch.from_numpy(y_test).type(torch.LongTensor).cuda())
else:
    X_train_tensor = Variable(torch.from_numpy(X_train))
    y_train_tensor = Variable(torch.from_numpy(y_train).type(torch.LongTensor))
    X_test_tensor = Variable(torch.from_numpy(X_test))
    y_test_tensor = Variable(torch.from_numpy(y_test).type(torch.LongTensor))
    

Batch_size = 100
iteration_number = 1e3

epochs_number = int(iteration_number / (len(X_train) / Batch_size))

# Pytorch train and test sets
Train_set = torch.utils.data.TensorDataset(X_train_tensor, y_train_tensor)
Test_set = torch.utils.data.TensorDataset(X_test_tensor, y_test_tensor)

# data loader
train_loader = torch.utils.data.DataLoader(Train_set, batch_size = Batch_size, shuffle = False)
test_loader = torch.utils.data.DataLoader(Train_set, batch_size = Batch_size, shuffle = False)

Artificial Neural Networks

Artificial neural networks (ANN), also know as connectionist systems, are computing system that is inspired by animal brain neural networks. ANNs are composed of artificial neurons. These neurons are connected using connections. For a given neuron, there are multiple input and output connections.

Artificial neural network components:

• Input Layer
• Hidden (Computation) Layers
• Output Layer

There is also an element of (machine) learning. Roughly speaking, learning consists of two parts forward propagation and Backpropagation. Together with a cost function, the algorithm runs iteratively with the object of decreasing Loss and increasing the accuracy.

In this article, we develop a Pytorch Artificial Neural Network model. The number of layers can be adjusted, of course. There are a large number of resources on choosing the right number of hidden layers such as [1]. Generally speaking, we do not recommend adding too many hidden layers. For a large number of problems, one hidden layer is sufficient.

PyTorch Artificial Neural Network with a Hidden Layer

A single hidden layer ANN in PyTorch can be defined as follows.

# Create ANN Model
class ANNModel_Single(nn.Module):
    def __init__(self, input_Size, hidden_Size, output_Size):
        super(ANNModel_Single, self).__init__()
        # Linear function 1:
        self.fc1 = nn.Linear(input_Size, hidden_Size) 
        # Non-linearity 1
        self.relu1 = nn.ReLU()
              
        # Linear function 4:
        self.fc2 = nn.Linear(hidden_Size, output_Size)  
    
    def forward(self, x):
        # Linear function 1
        out = self.fc1(x)
        # Non-linearity 1
        out = self.relu1(out)
        
        # Linear function 4 (readout)
        out = self.fc2(out)
        return out

input_Size, output_Size = len(X[0]), len(np.unique(y))
hidden_Size = 100

# model
model = ANNModel_Single(input_Size, hidden_Size, output_Size)

# GPU
if torch.cuda.is_available():
    model.cuda()

# Cross Entropy Loss 
CEL= nn.CrossEntropyLoss()

# Optimizer 
learning_rate = 1e-2
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)

# Traning the Model
Count = 0
Loss_list = []
Iteration_list = []
Accuracy_list = []
MSE_list = []
MAE_list = []
Steps = 10

Progress_Bar = progressbar.ProgressBar(maxval= iteration_number + 200,
                                       widgets=[progressbar.Bar('=', '|', '|'),
                                                progressbar.Percentage()])
# print('---------------------------------------------------------')
for epoch in range(epochs_number):
    for i, (Xtr, ytr) in enumerate(train_loader):
        
        # Variables
        Xtr = Variable(Xtr.view(-1, X[0].shape[0]))
        ytr = Variable(ytr)
        
        # Set all gradients to zero
        optimizer.zero_grad()
        
        # Forward
        Out = model(Xtr.float())
        
        # loss
        loss = CEL(Out, ytr.long())
        
        # Backward (Calculating the gradients)
        loss.backward()
        
        # Update parameters
        optimizer.step()
        
        Count += 1
        
        del Xtr, ytr
        
        # Predictions
        if Count % Steps == 0:
            # Calculate Accuracy         
            Correct, Total = 0, 0
            # Predictions
            for Xts, yts in test_loader: 
                Xts = Variable(Xts.view(-1, X[0].shape[0]))
                
                # Forward
                Out = model(Xts.float())
                
                # The maximum value of Out
                Predicted = torch.max(Out.data, 1)[1]
                
                # Total number of yts
                Total += len(yts)
                
                # Total Correct predictions
                Correct += (Predicted == yts).sum()
            del Xts, yts
            # storing loss and iteration
            Loss_list.append(loss.data)
            Iteration_list.append(Count)
            Accuracy_list.append(Correct / float(Total))
            
        Progress_Bar.update(Count)

Progress_Bar.finish()

history = pd.DataFrame({'Iteration': np.array(Iteration_list),
                      'Loss': np.array([x.cpu().data.numpy() for x in Loss_list]),
                      'Accuracy': np.array([x.cpu().data.numpy() for x in Accuracy_list])})
del Loss_list, Iteration_list, Accuracy_list

|=========================================================================|100%

Let's define some function by which we can analyze the performance of the modeling.

def Plot_history(history, Table_Rows = 25, yLim = 2):
    fig = make_subplots(rows=1, cols=2, horizontal_spacing = 0.02, column_widths=[0.6, 0.4],
                        specs=[[{"type": "scatter"},{"type": "table"}]])
    # Left
    fig.add_trace(go.Scatter(x= history['Iteration'].values, y= history['Loss'].astype(float).values.round(4),
                             line=dict(color='OrangeRed', width= 1.5), name = 'Loss'), 1, 1)
    fig.add_trace(go.Scatter(x= history['Iteration'].values, y= history['Accuracy'].astype(float).values,
                             line=dict(color='MidnightBlue', width= 1.5),  name = 'Accuracy'), 1, 1)
    fig.update_layout(legend=dict(x=0, y=1.1, traceorder='reversed', font_size=12),
                  dragmode='select', plot_bgcolor= 'white', height=600, hovermode='closest',
                  legend_orientation='h')
    fig.update_xaxes(range=[history.Iteration.min(), history.Iteration.max()],
                     showgrid=True, gridwidth=1, gridcolor='Lightgray',
                     showline=True, linewidth=1, linecolor='Lightgray', mirror=True, row=1, col=1)
    fig.update_yaxes(range=[0, yLim], showgrid=True, gridwidth=1, gridcolor='Lightgray',
                     showline=True, linewidth=1, linecolor='Lightgray', mirror=True, row=1, col=1)
    # Right
    ind = np.linspace(0, history.shape[0], Table_Rows, endpoint = False).round(0).astype(int)
    ind = np.append(ind, history.Iteration.values[-1])
    history = history[history.index.isin(ind)]
    fig.add_trace(go.Table(header=dict(values = list(history.columns), line_color='darkslategray',
                                       fill_color='DimGray', align=['center','center'],
                                       font=dict(color='white', size=12), height=25), columnwidth = [0.4, 0.4, 0.4, 0.4],
                           cells=dict(values=[history.Iteration, history.Loss.astype(float).round(4).values,
                                          history.Accuracy.astype(float).round(4).values],
                                      line_color='darkslategray', fill=dict(color=['WhiteSmoke', 'white']),
                                      align=['center', 'center'], font_size=12,height=20)), 1, 2)
    fig.show()
    
def Confusion_Matrix(Model, FG = (12, 4), X_train_tensor = X_train_tensor, y_train = y_train,
                     X_test_tensor = X_test_tensor, y_test = y_test):
    
    font = FontProperties()
    font.set_weight('bold')
    ############# Train Set #############
    fig, ax = plt.subplots(1, 2, figsize=FG)
    _ = fig.suptitle('Train Set', fontproperties=font, fontsize = 16)
    
    # Predictions
    y_pred = model(X_train_tensor.float())
    y_pred = torch.max(y_pred.data, 1)[1]
    y_pred = y_pred.cpu().data.numpy()
    
    # confusion matrix
    CM = metrics.confusion_matrix(y_train, y_pred)
    _ = sns.heatmap(CM.round(2), annot=True, annot_kws={"size": 14}, cmap="Blues", ax = ax[0])
    _ = ax[0].set_title('Confusion Matrix')
    CM = CM.astype('float') / CM.sum(axis=1)[:, np.newaxis]
    _ = sns.heatmap(CM.round(2), annot=True, annot_kws={"size": 14}, cmap="Greens", ax = ax[1],
                   linewidths = 0.2, vmin=0, vmax=1, cbar_kws={"shrink": 1})
    _ = ax[1].set_title('Normalized Confusion Matrix')
    
    for a in ax:
        _ = a.set_xlabel('Predicted labels')
        _ = a.set_ylabel('True labels')
        _ = a.xaxis.set_ticklabels(Labels)
        _ = a.yaxis.set_ticklabels(Labels)
        
    ############# Test Set #############
    fig, ax = plt.subplots(1, 2, figsize=FG)
    _ = fig.suptitle('Test Set', fontproperties=font, fontsize = 16)
    font = FontProperties()
    font.set_weight('bold')
    
    # Predictions
    y_pred = model(X_test_tensor.float())
    y_pred = torch.max(y_pred.data, 1)[1]
    y_pred = y_pred.cpu().data.numpy()
    
    # confusion matrix
    CM = metrics.confusion_matrix(y_test, y_pred)
    _ = sns.heatmap(CM.round(2), annot=True, annot_kws={"size": 14}, cmap="Blues", ax = ax[0])
    _ = ax[0].set_title('Confusion Matrix')
    CM = CM.astype('float') / CM.sum(axis=1)[:, np.newaxis]
    _ = sns.heatmap(CM.round(2), annot=True, annot_kws={"size": 14}, cmap="Greens", ax = ax[1],
                   linewidths = 0.2, vmin=0, vmax=1, cbar_kws={"shrink": 1})
    _ = ax[1].set_title('Normalized Confusion Matrix')
    
    for a in ax:
        _ = a.set_xlabel('Predicted labels')
        _ = a.set_ylabel('True labels')
        _ = a.xaxis.set_ticklabels(Labels)
        _ = a.yaxis.set_ticklabels(Labels)

def Plot_Classification(Model, X, y, Labels, BP = .5, Alpha=0.6, ax = False, fs = 7, ColorMap =  'Spectral'):
    h=0.02
    pad=0.25
    # adding margins
    x_min, x_max = X[:, 0].min()-pad, X[:, 0].max()+pad
    y_min, y_max = X[:, 1].min()-pad, X[:, 1].max()+pad
    # Generating meshgrids
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
    
    Temp = np.c_[xx.ravel(), yy.ravel()]
    if torch.cuda.is_available():
        Temp = Variable(torch.from_numpy(Temp).cuda())
    else:
        Temp = Variable(torch.from_numpy(Temp))
    # Predictions
    Pred = Model(Temp.float())
    Pred = torch.max(Pred.data, 1)[1]
    Pred = Pred.cpu().data.numpy()
    Pred = Pred.reshape(xx.shape)
    # Figure
    if ax == False:
        fig, ax = plt.subplots(1, 1, figsize=(fs, fs))
    _ = ax.contourf(xx, yy, Pred, cmap = ColorMap, alpha=0.2)
    
    scatter = ax.scatter(X[:,0], X[:,1], s=70, c=y, edgecolor = 'Navy', alpha = Alpha, cmap = ColorMap)
    _ = ax.legend(handles=scatter.legend_elements()[0], labels= Labels,
                  fancybox=True, framealpha=1, shadow=True, borderpad=BP, loc='best', fontsize = 14)
    _ = ax.set_xlim(x_min, x_max)
    _ = ax.set_ylim(y_min, y_max)
    _ = ax.set_xlabel(r'$X_1$')
    _ = ax.set_ylabel(r'$X_2$')

Model Optimization Plot

Plot_history(history, yLim = 1.6)

Confusion Matrix

The confusion matrix allows for visualization of the performance of an algorithm.

Confusion_Matrix(model)

Plot Classification

fig, ax = plt.subplots(1, 2, figsize=(16, 7))
# Train Set
Plot_Classification(model, X_train, y_train, Labels, ax = ax[0])
_ = ax[0].set_title('Train Set', fontsize = 16)
# Test Set
Plot_Classification(model, X_test, y_test, Labels, ax = ax[1])
_ = ax[1].set_title('Test Set', fontsize = 16)

for i in range(len(ax)):
    _ = ax[i].axis('off')

PyTorch Artificial Neural Network with Multiple Layers.

A three-layer ANN in PyTorch can be defined as follows.

# Create ANN Model
class ANNModel(nn.Module):
    def __init__(self, input_Size, hidden_Size, output_Size):
        super(ANNModel, self).__init__()
        # Linear function 1:
        self.fc1 = nn.Linear(input_Size, hidden_Size) 
        # Non-linearity 1
        self.relu1 = nn.ReLU()
        
        # Linear function 2:
        self.fc2 = nn.Linear(hidden_Size, hidden_Size)
        # Non-linearity 2
        self.tanh2 = nn.Tanh()
        
        # Linear function 3:
        self.fc3 = nn.Linear(hidden_Size, hidden_Size)
        # Non-linearity 3
        self.elu3 = nn.ELU()
        
        # Linear function 4:
        self.fc4 = nn.Linear(hidden_Size, output_Size)  
    
    def forward(self, x):
        # Linear function 1
        out = self.fc1(x)
        # Non-linearity 1
        out = self.relu1(out)
        
        # Linear function 2
        out = self.fc2(out)
        # Non-linearity 2
        out = self.tanh2(out)
        
        # Linear function 2
        out = self.fc3(out)
        # Non-linearity 2
        out = self.elu3(out)
        
        # Linear function 4 (readout)
        out = self.fc4(out)
        return out

input_Size, output_Size = len(X[0]), len(np.unique(y))
hidden_Size = 100

# model
model = ANNModel(input_Size, hidden_Size, output_Size)

# GPU
if torch.cuda.is_available():
    model.cuda()

# Cross Entropy Loss 
CEL= nn.CrossEntropyLoss()

# Optimizer 
learning_rate = 1e-2
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)

# Traning the Model
Count = 0
Loss_list = []
Iteration_list = []
Accuracy_list = []
MSE_list = []
MAE_list = []
Steps = 10

Progress_Bar = progressbar.ProgressBar(maxval= iteration_number + 200,
                                       widgets=[progressbar.Bar('=', '|', '|'),
                                                progressbar.Percentage()])
# print('---------------------------------------------------------')
for epoch in range(epochs_number):
    for i, (Xtr, ytr) in enumerate(train_loader):
        
        # Variables
        Xtr = Variable(Xtr.view(-1, X[0].shape[0]))
        ytr = Variable(ytr)
        
        # Set all gradients to zero
        optimizer.zero_grad()
        
        # Forward
        Out = model(Xtr.float())
        
        # loss
        loss = CEL(Out, ytr.long())
        
        # Backward (Calculating the gradients)
        loss.backward()
        
        # Update parameters
        optimizer.step()
        
        Count += 1
        
        del Xtr, ytr
        
        # Predictions
        if Count % Steps == 0:
            # Calculate Accuracy         
            Correct, Total = 0, 0
            # Predictions
            for Xts, yts in test_loader: 
                Xts = Variable(Xts.view(-1, X[0].shape[0]))
                
                # Forward
                Out = model(Xts.float())
                
                # The maximum value of Out
                Predicted = torch.max(Out.data, 1)[1]
                
                # Total number of yts
                Total += len(yts)
                
                # Total Correct predictions
                Correct += (Predicted == yts).sum()
            del Xts, yts
            # storing loss and iteration
            Loss_list.append(loss.data)
            Iteration_list.append(Count)
            Accuracy_list.append(Correct / float(Total))
            
        Progress_Bar.update(Count)

Progress_Bar.finish()

history = pd.DataFrame({'Iteration': np.array(Iteration_list),
                      'Loss': np.array([x.cpu().data.numpy() for x in Loss_list]),
                      'Accuracy': np.array([x.cpu().data.numpy() for x in Accuracy_list])})
del Loss_list, Iteration_list, Accuracy_list

|=========================================================================|100%

Model Optimization Plot

Plot_history(history, yLim = 1.6)

Confusion Matrix

The confusion matrix allows for visualization of the performance of an algorithm.

Confusion_Matrix(model)

Plot Classification

fig, ax = plt.subplots(1, 2, figsize=(16, 7))
# Train Set
Plot_Classification(model, X_train, y_train, Labels, ax = ax[0])
_ = ax[0].set_title('Train Set', fontsize = 16)
# Test Set
Plot_Classification(model, X_test, y_test, Labels, ax = ax[1])
_ = ax[1].set_title('Test Set', fontsize = 16)

for i in range(len(ax)):
    _ = ax[i].axis('off')

---

Refrences

1. Stathakis, D. (2009). How many hidden layers and nodes?. International Journal of Remote Sensing, 30(8), 2133-2147.
2. Artificial neural network. Retrieved June 02, 2020, from https://en.wikipedia.org/wiki/Artificial_neural_network.

---